Two stars are at rest with respect to each other separated by a distance of 12 l

Question

Two stars are at rest with respect to each other separated by a distance of 12 light-years as measured by observers at rest with respect to the stars. Observers in the stars observe an astronaut fly from one star to the other with a speed of v = 0.6c. How long did the trip last as measured by the observers at rest with respect to the stars?

[A] 12 years. [B] 12.8 years. [C] 16 years [D] 20 years [E] 25 years.

In the problem above, how long did the trip last as measured by the astronaut?

[A] 12 years. [B] 12.8 years. [C] 25 years [D] 20 years [E] 1years.

In the problem above, what is the distance between the stars as measured by the astronaut?

[A] 12 light-years. [B] 15 light-years. [C] 16 light-years [D] 9.6 light-years. [E] 7.2 light-years

Explanation / Answer

d = 12 light years = 12c*year, v =0.6c

(a) time = distance/velocity

= 12c*year/0.6c = 20 years

correct option is (D)

(b) from special theory of relativity

t = to/gamma

t = to(1-v^2/c^2)^0.5

t = 20*(1-0.6^2)^0.5

t = 16 years

correct option is (E)

(c) d = do*gamma = do/(1-v^2/c^2)^0.5

d =12/(1-0.6^2)^0.5

d = 15 light years

correct option is (B)

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